IP addresses
IP address is the device's unique identifier in the network. It works on 3rd layer of OSI, The Network layer. It uses Best-effort delivery, meaning it has no guarantee data won't be lost on the way, which is mitigated by The Transport layer protocols.
It has two common standards: IPv4 and IPv6.
IPv4
IPv4 addresses can be represented in any notation by 32-bit number.
IP addresses can be public and private. Private IP addresses:
10.0.0.0/8
172.16.0.0/12
192.168.0.0/16
There's other reserved ranges:
0.0.0.0/8 - current network
100.64.0.0/10 - shared address space used by ISPs
127.0.0.0/8 - loopback interface
169.254.0.0/16 - link-local addresses (for when IP is not specified, like when retrieving it from a DHCP server)
192.88.99.0/24 - formerly used for IPv6 to IPv4 relay
255.255.255.255/32 - limited broadcast
…and so on.
IPv6
IPv6 was intended to replace IPv4. It uses 128-bit addresses. Direct communication between IPv6 and IPv4 is impossible, though there are some transition mechanism to help with that.
IPv6 simplifies many aspects, so it's faster than IPv4.